# File

```Chapter 1 Review
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1.1 Connect English With Mathematics and Graphing Lines
1. Translate each sentence into an equation. Tell how you are assigning the variables in each.
a) Three consecutive numbers add to 75.
b) Stephane has loonies and toonies in his
pocket totalling \$25.
c) Three times Jennifer’s age is 26 more
than Herbert’s age.
2. Write a system of equations for each situation.
a) Michael is three times older than his sister
Angela. In 1 year, Michael will be twice
as old as Angela. How old are the two
children today?
b) A \$2 raffle ticket offers a bonus \$1 early
bird draw. 400 tickets were sold for the
draw and a total of \$894 was collected
from ticket sales. How many tickets were
bought for \$2 and how many were bought
for \$3?
3. Graph each pair of lines to find their point of intersection.
a) y = x  5
y=3x
b) y = 3x + 8
x + 2y = 2
c) 2x  y =  4
2x + y = 6
d) 3x  2y = 8
x  2y =  4
1.2 The Method of Substitution
4. Solve each linear system using the method of substitution.
a) 2x + y = 7
3x  2y = 21
b) y = 2x + 4
x  4y = 9
c) 3s + 5t = 2
s + 4t =  4
d) 3m  6n = 1
m + 3n = 2
Principles of Mathematics 10: Teacher’s Resource
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5. Is the point (3, 5) the solution to each system of linear equations? Explain.
a) 2x  y = 1
3x + 4y = 29
b) x + y = 8
2x  y = 1
6. The two largest deserts in the world are the Sahara Desert and the Australian Desert.
The sum of their areas is 13 million square kilometres. The area of the Sahara Desert is 5 million
square kilometres more than the area of the Australian Desert. Write and solve a system of
equations to find the area of each desert.
1.3 Investigate Equivalent Linear Relations and Equivalent Linear Systems
2
1
7. Which of the following equations is equivalent to y = x  ?
3
5
A y = 2x + 1
B 3y = 2x + 1
C 15y = 10x + 3
D 10x  15y + 5 = 0
8. A linear system is given.
1
y = x3

5
2
y =  x 1

7
a) Explain why the following is an
equivalent linear system.
x  5y = 15

2x + 7y = 7

b) If you graph all four lines, what result do
you expect? Graph to check.
9. The two most common place names in Canada are Mount Pleasant and Centreville. The total
number of places with these names is 31. The number of places called Centreville is one less than
the number of places called Mount Pleasant. Write and solve a system of equations to find the
number of places in Canada with each name.
1.4 The Method of Elimination
10. Solve each linear system. Check each solution.
a) x  y = 14
2x + 5y = 7
b) 2x  3y =  4
3x + y = 5
c) 3x + 4y = 17
7x  2y = 17
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d) 2x + 5y = 18
3x + 5y  17 = 0
11. Simplify and solve each system of equations using elimination.
a) 2(x  4) + 3(y + 2) = 8
4(x + 1) + 5(y  1) = 9
b) 0.4x  0.1y = 0.6
1.8x + 0.4y = 4.4
12. Cindy buys a large pizza with two toppings for \$13.50. Lou buys three large pizzas with four
toppings each at the same pizza parlour for \$45. Find the cost of a large pizza and the cost per
topping.
1.5 Solve Problems Using Linear Systems
13. A chemist needs 10 L of 21% salt solution. The chemist has two salt solutions available at 15%
and 25% salt. Write and solve a linear system to find the volume of each solution that needs to be
combined to make the mixture.
14. Flying into the wind, a plane takes 6 h to fly 3000 km. On the return flight, with the same wind,
the plane takes 5 h to complete the trip. How fast does the plane fly without any wind, and how
fast was the wind blowing?
15. The public golf course runs a junior league with a registration fee of \$200 and a cost of \$25 per
round played. To stay competitive, the private golf club in the same town offers a junior league
with a registration fee of \$250, but only \$20 per round played.
a) Write linear equations to represent both
junior leagues.
b) Solve the linear system.
c) Interpret the solution.
d) Which league should each golfer join?
i) MaeLing plans to play 16 rounds in
the league.
ii) Jacob plans to play 8 rounds in the
league.
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Chapter 2 Review
2.1 Midpoint of a Line Segment
1. Find the midpoint of each line segment.
a)
b)
2. a) Determine the midpoint of the line
segment with endpoints E(6, 7) and
F(2, 1).
b) Determine the midpoint of the line
segment with endpoints E(5, 9) and
F(2, 4).
3. a) Draw the triangle with vertices A(5, 2),
B(1,  4), and C(3, 3).
b) Draw the median from vertex A. Then,
find an equation in the form y = mx + b
for this median.
c) Draw the right bisector of AC. Then, find
an equation in the form y = mx + b for this
right bisector.
d) Draw the altitude from vertex C. Then,
find an equation in the form y = mx + b
for this altitude.
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2.2 Length of a Line Segment
4. Determine the length of the line segment
defined by each pair of points.
a) R(5, 6) and S(2, 6)
b) T(4, 5) and U(4, 5)
c) M(5, 6) and N(3, 4)
d) P(2, 6) and Q(7, 3)
5. a) Determine the length of the median from
vertex R of PQR.
b) Determine the perimeter of PQR.
of a unit.
6. a) Draw the triangle with vertices X(1, 4),
Y(3, 2), and Z(3, 6).
b) Use analytic geometry to show that
XYZ = 90&deg;.
c) Determine the area of XYZ.
2.3 Apply Slope, Midpoint, and Length
Formulas
7. Show that the triangle with vertices P(1, 0),
Q(0, 3 ), and R(1, 0) is equilateral.
8.
a) Show algebraically that this triangle is
isosceles.
b) Find the midpoints of the equal sides.
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c) Show algebraically that the line segment
joining the midpoints of the equal sides is
parallel to the third side of the triangle.
9. On a map, a ski hill has a chair lift running
straight from A(30, 25) to B(60, 55).
a) How long is the section of the chair lift if
each unit on the map grid represents 1 m,
to the nearest tenth of a metre?
b) Is the point C(50, 45) on the chair lift?
2.4 Equation for a Circle
10. Determine an equation for each circle.
a)
b)
c)
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11. Find an equation for the circle that is centred
at the origin and
a) has a radius of 3.7
b) has a radius of 8
c) has a diameter of 18
d) passes through the point (3, 5)
12. a) Show that the line segment joining
C(2, 5) and D(5, 2) is a chord of the
b) Determine an equation for the right
bisector of the chord CD.
circle defined by x2 + y2 = 29.
13. a) Show that point B(3, 2) lies on the
circle defined by x2 + y2 = 13.
b) Find an equation for the radius from the
origin O to point B.
c) Find an equation for the line that passes
through B and is perpendicular to OB.
Chapter 3 Review
3.1 Investigate Properties of Triangles
1. a) Define an altitude.
b) List two additional properties of the
altitudes of a triangle.
c) Outline how you could use geometry
software to show that the altitudes of all
triangles have these properties.
2. a) Show that ABC with vertices A(3, 3),
B(1, 5), and C(1, 3) is isosceles.
b) Find the midpoint, M, of side AB and the
midpoint, N, of side BC.
c) Verify that the lengths of the medians of
the two equal sides of the isosceles
triangle are equal.
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3.2 Verify Properties of Triangles
3. a) Verify that PQR is a right triangle.
b) Describe another method that you could
use to verify that PQR is a right
triangle.
4. a) Classify XYZ. Explain your reasoning.
b) Verify that the altitude from vertex X
bisects side YZ in XYZ.
5. A triangle has vertices K(–2, 2), L(1, 5), and
M(3, –3). Verify that
a) the triangle has a right angle
b) the midpoint of the hypotenuse is
equidistant from each vertex
6. a) Verify that the diagonals of a square are
equal and bisect each other at right
b) Verify that the diagonals of a
parallelogram bisect each other. Explain
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c) Verify that the diagonals of a kite meet
each other at right angles and one
diagonal bisects the other diagonal.
7. a) Draw any parallelogram ABCD.
b) Show that ABC  CDA. Explain
8. Use Technology Use geometry software to
9. Verify that quadrilateral DEFG is a parallelogram.
10. Verify that the quadrilateral with vertices
P(2, 3), Q(5, –1), R(10, –1), and S(7, 3) is
a rhombus.
11. a) Draw the quadrilateral with vertices
P(3, 4), Q(2, 6), R(0, 5), and S(1, 3).
b) Classify quadrilateral PQRS. Justify this
classification.
c) Verify a property of the diagonals of
12. A quadrilateral has vertices K(–1, 4), L(2, 2),
M(0, –1), and N(–3, 1). Verify that
a) KLMN is a square
b) each diagonal of KLMN is the
perpendicular bisector of the other
diagonal
c) the diagonals of KLMN are equal in
length
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3.5 Properties of Circles
13. a) Show that X( 4, 3) and Y(4, 3) are
endpoints of a diameter of the circle
x2 + y2 = 25.
b) State the coordinates of another point Z,
with integer coordinates, on the circle
x2 + y2 = 25.
c) Show that XYZ is a right triangle.
14. a) Verify that the points D(2, 5) and
E(5, 2) lie on the circle with equation
x2 + y2 = 29.
b) Verify that the right bisector of the chord
DE passes through the centre of the circle.
15. Find the centre of the circle that passes
through the points P(–9, 5), Q(1, 5), and
R(–2, –2).
16. Use Technology Use geometry software to
Chapter 4 Review
4.1 Investigate Non-Linear Relations
1. Identify whether each scatter plot can be modelled using a line of best fit or a curve of best fit.
a
)
b
)
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11)
2. Use the data in the table to answer the questions below.
Time (years)
0
1
2
3
4
5
6
7
8
9
Value of the
Investment (\$)
100
105
108
114
121
135
150
171
195
225
a) Make a scatter plot of the data and draw
a curve of best fit.
b) Describe the relation between value and
time.
c) Use your curve of best fit to estimate the
value of the investment after 10 years.
3. Use finite differences to determine whether each relation is linear, quadratic, or neither.
a)
b)
c)
x
1
2
3
4
5
x
2
1
0
1
2
x
1
3
5
7
9
y
3
10
29
66
127
y
12
3
0
3
12
y
5
13
21
29
37
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12)
4.
Susan throws a rock off a cliff that is
210 m tall. The height, h, in metres, of
the rock above the ground can be related
to the time, t, in seconds by the
equation h = 5t2 + 10t + 210.
a) Graph the relation.
b) What is the maximum height of the rock?
c) When does the rock reach its maximum
height?
4.3 Investigate Transformations of Quadratics and 4.4 Graph y = a(x  h)2 + k
5. Sketch the graph of each parabola and describe its transformations from the relation
y = x2.
a) y = (x + 3)2 b) y = x2 + 2
1
c) y = x 2
d) y = 3x2
3
6. Copy and complete the table for each
parabola. Replace the heading for the second column with the equation for the parabola.
a) y = (x + 2)2 + 3
b) y = 4(x  5)2  1
c) y =  1 ( x  2)2  3
3
d) y = (x  3)2  4
Property
vertex
y = a(x  h)2 + k
axis of symmetry
stretch or
compression
direction of opening
values that x may
take
values that y may
take
7. Sketch each parabola in question 6.
8. A store can increase revenue by increasing the price of its T-shirts. The revenue, R, in dollars,
can be modelled by the relation
R = 50(d  3.5)2 + 4000, where d represents the dollar increase in price.
a) Graph the relation for 0  d  10.
b) What is the maximum revenue?
c) What dollar increase corresponds to the
maximum revenue?
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13)
4.5 Quadratic Relations of the Form
y = a(x  r)(x  s)
9. Sketch a graph for each quadratic relation. Label the vertex and the x-intercepts.
a) y = (x  2)(x + 6)
1
b) y = ( x  8)( x  2)
2
c) y = x(x + 10)
10. The path of a jet plane in training manoeuvres is given by the relation
h = 5(t + 20)(t  100), where h represents the height, in metres, above the ground and
t is time, in seconds.
a) Sketch a graph for this relation.
b) At what time does the plane reach its
maximum height?
c) What is the maximum height?
4.6 Negative and Zero Exponents
11. Evaluate.
a) 63
b) 82
 
c)   2
3
0
e) (3)2
g) 70
12. Evaluate.
a) 62  61
13. Solve for x.
1
a) 3x =
27

f)   3 
5
h)   1 
3
d) 1
2
4
3
3
c) 42 + 41
b) (4 + 5)0

x
b) 2 = 25
5
4
27
c) x 3 =
64
14. The half-life of sodium-24 is 16 h.
a) What fraction of a sample of sodium-24
will remain after 32 h?
b) What fraction of a sample of sodium-24
will remain after 4 days?
c) Write the fractions in parts a) and b) with
a negative exponent with a base of 2.
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14)
Chapter 5 Review
5.1 Multiply Polynomials
1. Use the distributive property to find each binomial product.
a) (x + 7)(x + 3)
b) (y  3)(y + 5)
c) (x  3y)(x + 2y) d) (3a + 8b)(5a + 6b)
2. Expand and simplify.
a) 4(a + 6)(a  3)
b) 3x(x + 2y)(x + 6y)
c) (10y + 6)(3y + 7)  (y + 2)(y  4)
d) 2b(4b  7)(3b + 2)  b(5b + 2)(b  6)
e) x(x + y)(2x + y)  y(3x + y)(x  y)
3. A parabola has equation y = 2(x  3)(x  6).
a) Expand and simplify the right side of
the equation.
b) State the x-intercepts of the parabola.
c) Verify in the expanded form that these
are the x-intercepts.
4. a) Write a simplified algebraic expression
to represent the area of the figure.
b) Expand and simplify your expression
from part a).
5.2 Special Products
5. Draw a diagram to illustrate each product.
a) (x + 5)2
b) (y + 3)2
6. Expand and simplify.
a) (x + 6)2
b) (r  3)2
c) (y + 10)2
d) (e  5)2
7. Expand and simplify.
a) (b + 9)(b  9)
b) (y  11)(y + 11)
c) (m + 13)(m  13) d) (14  x)(14 + x)
8. Expand and simplify.
a) (x  3y)2
b) 5(2x + 5b)2
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c) (11x  13y)(11x + 13y)
d) (a  6b)(a + 6b)
9. A square has side length 4a. One dimension
is increased by 6 and the other is decreased by 6.
a) Write an algebraic expression to represent
the area of the resulting rectangle.
b) Expand this expression and simplify.
c) Write and simplify an algebraic expression
for the change in area from the square to
the rectangle.
d) Calculate the new area of the rectangle
if a represents 5 cm.
5.3 Common Factors
10. Use algebra tiles or a diagram to illustrate the factoring of each polynomial.
a) x2 + 5x
b) 8x2 + x
11. Factor.
a) 2x2 + 4x
c) 10x2 + 20y2
b) 5x2 + 3x
d) 3xy  7xz
12. Factor by grouping.
a) 2x2 + 2x + 3xy + 3y
b) x3 + x2y + yx + y2
c) 5ab  5a + 3b  3
d) 3a2x + 3a2y + b2x + b2y
13. Factor, if possible.
a) 2z(x + y) + 3xy(x + y)
b) x2 + y2 + z2
c) 6a3 + 3a2 + 12a + 6
d) x2yz2  x2z2 + xyz
14. Write an expression in fully factored form for the shaded area.
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5.4 Factor Quadratic Expressions of the Form x2 + bx + c
15. Illustrate the factoring of each trinomial using algebra tiles or a diagram.
a) x2 + 6x + 9
b) x2 + 12x + 35
16. Factor.
a) x2  4x  12
b) x2  7x + 12
c) x2  4x  45
d) x2 + 9x + 14
17. Factor completely by first removing the greatest common factor (GCF).
a) 2x2 + 16x  30
b) x3 + 3x2  28x
18. Determine binomials to represent the length and width of the rectangle, and then determine the
dimensions of the rectangle if x = 11 cm.
5.5 Factor Quadratic Expressions of the Form ax2 + bx + c
19. Factor, using algebra tiles or a diagram if necessary.
a) 12x2  5x  3
b) 3x2  13x  10
c) 10x2 + 9x  7
d) 21x2 + 4x  1
20. Factor, if possible.
a) 3x2 + 15y + 33
b) 2x2 + 7x + 9
c) 30x2 + 9x  12
d) 6x2  34x + 12
21. Find a value of k so that each trinomial can be factored over the integers.
a) 3x2 + kx  10
b) 24x2 + 47x + k
5.6 Factor a Perfect Square Trinomial and
a Difference of Squares
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22. Factor fully.
a) x2  100
c) 9x2  16
e) 1  225y2
b) c2  25
d) 128  18x2
f) 3x2 + 27y2
23. Verify that each trinomial is a perfect square, and then factor.
a) y2 + 16y + 64 b) x2  20x + 100
c) 225  90y + 9y2 d) 121c2 + 308cd + 196d2
24. Factor, if possible.
a) 9y2 + 24y  16
b) 50x2  60xy + 18y2
2
2
c) (x  3)  (y  4) d) x2 + 9y2
25. A rectangular prism has a volume of
4x3 + 12x2 + 9x.
a) Determine algebraic expressions for the
dimensions of the prism.
b) Describe the faces of the prism.
c) Determine the volume if x = 3 cm.
d) Determine the surface area if x = 3 cm.
Chapter 6 Review
6.1 Minima and Maxima
1. Rewrite each relation in the form
y = a(x  h)2 + k by completing the square. Use algebra tiles or a diagram to support your
solution.
a) y = x2 + 6x + 3
b) y = x2 + 4x  1
c) y = x2 + 8x + 7
d) y = x2 + 10x  5
2. Find the vertex of each quadratic relation. Sketch a graph of the relation, labelling the vertex, the
axis of symmetry, and two other points.
a) y = x2 + 14x  7
b) y = x2 + 6x + 1
c) y = 2x2 + 12x + 4
d) y = x2 + 16x + 3
3. Use a graphing calculator to find the minimum or maximum value for each quadratic relation.
a) y = 2x2 + 3x + 5
b) y = 0.3x2 + 0.9x + 9
1
1
1
c) y  x 2  x 
4
8
4
2
d) y = 2x + 8x + 5
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4. The path of a basketball can be modelled by
the equation h = 0.06d2 + 0.6d + 3, where
h represents the height, in metres, of the ball above the ground and d represents the
horizontal distance, in metres, that the ball travels.
a) What is the maximum height reached by
the ball?
b) What horizontal distance has the ball
travelled when it reaches this maximum
height?
5. Solve by factoring. Check your solutions.
a) x2 + 2x  15 = 0
b) m2  13m + 36 = 0
c) 4y2  8y  5 = 0
d) 15c2  8c  12 = 0
6. Solve.
a) y2 + 2y = 8
b) 5x2 = 8x  3
c) 4z2 = 1
d) 10m2  40m = 0
e) 8x2  40 = 22x
f) 18x2 + 39x = 15
7. Write a quadratic equation in the form
ax2 + bx + c = 0, where a, b, and c are integers, given the following roots.
a) 5 and 3
1
2
b)  and
3
5
6.3 Graph Quadratics Using the x-Intercepts
8. Find the x-intercepts and the vertex of each
a) y = x2 + 6x + 9
b) y = 25x2  9
c) y = x2 + 4x + 21
d) y = x2 + 12x + 32
e) y = 2x2 + 4x + 48
f) y = 20x2  5
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9. Write an equation in the form
y = ax2 + bx + c to represent each parabola.
a)
b)
c)
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d)
10. A parabola has a vertex (3, 4) and one
x-intercept is 1. Find the other x-intercept and the y-intercept.
a) x2 + 5x + 2 = 0
b) 3x2 + x  1 = 0
c) x2  6x + 4 = 0
d) 5x2  3x  4 = 0
e) 2x2 + 3x – 7 = 0
f) 3x2 – x – 1 = 0
g) 2x2 + x – 5 = 0
h) 0 = –3x2 + 3x + 1
12. For each quadratic relation, state the
coordinates of the vertex and the direction of opening and determine the number of
x-intercepts.
a) y = 3(x + 1)2 + 1
b) y   1 ( x  2)2  3
2
2
c) y  ( x  3) 2
3
d) y = 3(x + 4)2  2
13. A toy rocket is launched from a platform that is 2 m off the ground at an initial velocity of 17.4
m/s. The height, h, in metres, of the rocket t seconds after it is launched is given by the equation h
= 4.9t2 + 17.4t + 2.
a) How long will it take the toy rocket to
reach a height of 9 m, to the nearest tenth
of a second?
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b) When will the toy rocket fall back to the
height of 9 m, to the nearest tenth of a
second?
find the time when the rocket will reach
its maximum height and determine this
maximum height. Round to the nearest
tenth.
6.5 Solve Problems Using Quadratic Equations
14. If the product of two consecutive even numbers is 8648, what are the two numbers?
15. A garden against the wall of a house is to be surrounded on three sides by a total of 336 m of
fencing. What dimensions of the garden will result in an area of 14 112 m2?
16. If part of a photograph is used to fill an
available space in a book or magazine, the photograph is said to be cropped. A photograph that
was originally 15 cm by
10 cm is cropped by removing the same width from the top and the left side. Cropping reduces
the area of the photograph by 46 cm2. What are the dimensions of the cropped photograph?
17. A set of p non-collinear points (points not in
a straight line) can be connected by a maximum of
p2  p
line segments.
2
a) Find the number of non-collinear points
that can be connected by a maximum of
55 line segments.
b) Is it possible for a set of non-collinear
points to be connected by a maximum of
40 line segments?
18. The acceleration due to gravity on Earth is 9.8 m/s2. A tennis ball is hit into the air at an initial
velocity of 25 m/s from a height of
0.7 m above the ground.
a) Write an equation for the height, h, in
metres, of the tennis ball in terms of the
time, t, in seconds, it has been in the air.
b) Find the height of the tennis ball 1.5 s
after it was hit, to the nearest tenth of a
metre.
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c) Find the maximum height of the tennis
ball and when it occurs. Round to the
nearest tenth.
19. Need-a-Ride is a car rental agency that rents
400 cars a week at \$80 per car. Industry research has shown that for every \$2 increase in rental
price, an agency will rent eight fewer cars.
a) Total revenue is the product of the price
per rental and the number of vehicles
rented. Write an expression to represent
the revenue for the rental agency.
b) Find the maximum revenue.
c) For this revenue, how many cars are
rented and how much is the rental price
per car?
Chapter 7 Review
7.1 Investigate Properties of Similar Triangles
1. a) Draw two triangles that are similar.
b) Draw two hexagons that are congruent.
2. Name the two similar triangles and explain why they are similar.
a)
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b)
7.2 Use Similar Triangles to Solve Problems
3. The pairs of triangles are similar. Find the
unknown side lengths.
a)
b)
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4.
The tips of the shadows of a flagpole and a
1.5-m fence post meet at the point S. The following lengths are measured: ST = 2.7 m and QT =
7.4 m. Use this information to find the height of the flagpole. Round your answer to the nearest
tenth of a metre.
5. Nimo has constructed a deck in the shape of
an equilateral triangle with each side length equal to 2 m. If she enlarges her deck to a similar shape
whose side lengths are doubled, what will the area of the new deck be?
7.3 The Tangent Ratio
6. Find the tangent of A, to four decimal
places.
a)
b)
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7.
Find the measure of each angle, to the
nearest degree.
a) tan  = 0.8173
b) tan E = 1.5413
13
c) tan  =
18
23
d) tan B =
12
8. Find x, to the nearest tenth of a metre.
a)
b)
9. The angle of elevation of a ramp is 4&deg;.
The horizontal length of the ramp is 18 m. What is the vertical height of the ramp, to the nearest
tenth of a metre?
7.4 The Sine and Cosine Ratios
10. Find sin , cos , and tan  for each triangle,
expressed as fractions in lowest terms.
a)
b)
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11. Find the measure of each angle, to the
nearest degree.
a) sin  = 0.4152
b) sin T = 0.8731
11
c) cos  =
15
3
d) cos S =
8
12. Find x, to the nearest tenth of a metre.
a)
b)
13. Solve PQR. Round angles to the nearest
degree.
7.5 Solve Problems Involving Right Triangles
14. Solve each triangle. Round side lengths to
the nearest tenth of a unit.
a)
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b)
15. Find the length of x, to the nearest tenth of a
centimetre.
16. The Carziz Tunnel cuts through Mount
Mainet. At the start of the tunnel, the angle of elevation of the top of Mount Mainet is 38&deg;. At the
end of the tunnel, the angle of elevation of the top of Mount Mainet is 42&deg;. The height of Mount
Mainet above the tunnel passage is 584 m. How long is the Carziz tunnel through Mount Mainet?
Chapter 8 Review
8.1 The Sine Law
1. Find a, to the nearest tenth of a centimetre.
a)
b) In DEF, D = 73&deg;, E = 64&deg;, and
d = 9.0 m.
2. Find the measure of P, to the nearest
degree.
3. Solve each triangle. Round answers to the
nearest tenth of a unit.
Principles of Mathematics 10: Teacher’s Resource
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4. Three trees are in the yard at the back of
Aly’s house. The oak tree is 10 m from the
ash tree and 15 m from the maple tree. The
line from the oak tree to the ash tree and the
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line from the ash tree to the maple tree form
an angle of 78&deg;.
a) Draw a diagram and label the known
information.
b) How far apart are the ash tree and the
nearest tenth of a metre.
8.3 Find Angles Using the Cosine Law
7. Find the measure of S, to the nearest
degree.
8.2 The Cosine Law
5. Find d, to the nearest tenth of a centimetre.
8. Solve each triangle. Round answers to the
nearest tenth of a degree.
a)
6. Solve each triangle. Round answers to the
nearest tenth of a unit.
a)
b) In acute BXR, b = 5.2 cm, x = 6.3 cm,
and r = 7.1 cm.
b) In acute RGM, M = 78&deg;, r = 10 cm,
and g = 13 cm.
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8.4 Solve Problems Using Trigonometry
9. Cara is standing in the centre of a field. From
where she is standing, she can see four posts
at different positions on the field, as shown
in the diagram. How far apart are posts A
and B, to the nearest tenth of a metre?
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